We provide an accurate closed-form expression for the expected shortfall of linear portfolios with elliptically distributed risk factors. Our results aim to correct inaccuracies that originate in and are present also in at least thirty other papers referencing it, including the recent survey on...

We study a class of backtests for forecast distributions in which the test statistic is a spectral transformation that weights exceedance events by a function of the modeled probability level. The choice of the kernel function makes explicit the user's priorities for model performance. The class...

Using only daily data on bond and stock returns, we identify and characterize flight to safety (FTS) episodes for 23 countries. On average, FTS days comprise less than 3% of the sample, and bond returns exceed equity returns by 2.5 to 4%. The majority of FTS events are country-specific not...

Changes in monetary policy have surprisingly strong effects on forward real rates in the distant future. A 100 basis-point increase in the 2-year nominal yield on an FOMC announcement day is associated with a 42 basis-point increase in the 10-year forward real rate. This finding is at odds with...

This paper introduces the "compound confluent hypergeometric" (CCH) distribution. The CCH unifies and generalizes three recently introduced generalizations of the beta distribution: the Gauss hypergeometric (GH) distribution of Armero and Bayarri (1994), the generalized beta (GB) distribution of...

While many studies find that the tail distribution of high frequency stock returns follow a power law, there are only a few explanations for this finding. This study presents evidence that time-varying volatility can account for the power law property of high frequency stock returns. The power...

This paper develops a framework for measuring digital services in the face of ongoing innovations in the delivery of content to consumers. We capture what Brynjolfsson and Saunders (2009) call "free goods" as the capital services generated by connected consumers' stocks of IT digital goods; this...

This paper studies the consequences of asset bubbles for economies that are vulnerable to persistent stagnation. Stagnation is the result of a shortage of assets that creates an oversupply of savings and puts downward pressure on the level of interest rates. Once the zero lower bound on the...

We estimate a reduced-form model of credit risk that incorporates stochastic volatility in default intensity via stochastic time-change. Our Bayesian MCMC estimation method overcomes nonlinearity in the measurement equation and state-dependent volatility in the state equation. We implement on...

We estimate asset pricing models with multiple risks: long-run growth, long-run volatility, habit, and a residual. The Bayesian estimation accounts for the entire likelihood of consumption, dividends, and the price-dividend ratio. We find that the residual represents at least 80% of the variance...